Photonic crystal optical waveguide

ABSTRACT

A photonic crystal optical waveguide includes a optical waveguide portion having a core made of a photonic crystal with a structure having a periodic refractive index in at least one direction perpendicular to a propagation direction of guided light and having a uniform refractive index in the propagation direction of the guided light, and a cladding arranged in contact with the core, in order to confine the guided light in the core, and an incident-side phase modulation portion arranged in close proximity or in contact with an incident surface of the core.

TECHNICAL FIELD

The present invention relates to optical waveguides using photoniccrystals.

BACKGROUND ART

In recent years, research and development of new optical fibers referredto as holey fibers or photonic crystal fibers have progressed at adramatic pace. In conventional optical fibers, the light is confined tothe core portion by a simple refractive index difference. In contrast,these new optical fibers are characterized by having a complicatedtwo-dimensional structure in their cross section. For example, the lightcan be confined in the core portion by establishing a refractive indexdifference between the cladding portion and the core portion by reducingthe effective refractive index in the cladding portion through thearrangement of holes in the cladding portion. Alternatively, the lightcan be confined in the core portion by forming a photonic band gap withrespect to the guided light in the core portion through making thecladding portion of a photonic crystal. Optical fibers are constitutedby such means.

It is possible to change the characteristics of holey fibers andphotonic crystal fibers considerably through their structure, so thatapplications such as dispersion compensation optical fibers withincreased wavelength dispersion, optical fibers with large non-linearoptical effects and zero dispersion optical fibers with zero dispersionin the visible spectrum have been proposed. Moreover, the complicatedtwo-dimensional structures can be fabricated for example by heating andstretching a plurality of quartz pipes that are bundled together (seefor example “O Plus E”, vol. 23, No. 9, p. 1061, 2001)

In the holey fibers and photonic crystal fibers that have been proposedso far, single mode propagation with the 0-th mode is used for theguided light propagating through the core portion. In single modepropagation, there are extremely little changes of the refractive indexwith respect to the frequency. Consequently, it is not possible toattain the characteristics of group velocity anomalies or very largedispersion. Therefore, even though single mode propagation is anecessary condition to prevent wavelength dispersion due to multi-modepropagation, at the same time it also poses restrictions with regard tothe core cross section area and the optical fiber performance.

DISCLOSURE OF THE INVENTION

It is an object of the present invention to solve the problems of theprior art and to provide a photonic crystal optical waveguide that canpropagate the desired band propagation light.

A photonic crystal optical waveguide in accordance with the presentinvention includes a optical waveguide portion having a core made of aphotonic crystal with a structure having a periodic refractive index inat least one direction perpendicular to a propagation direction ofguided light and having a uniform refractive index in the propagationdirection of the guided light, and a cladding arranged in contact withthe core, in order to confine the guided light in the core, and anincident-side phase modulation portion arranged in close proximity or incontact with an incident surface of the core.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a cross-sectional view showing a one-dimensional photoniccrystal.

FIG. 2 is a band graph showing the photonic band structure of the TEpolarized light in the one-dimensional photonic crystal.

FIG. 3 is a band graph showing the photonic band structure of the TMpolarized light in the one-dimensional photonic crystal.

FIG. 4 is a perspective view showing the configuration of a photoniccrystal optical waveguide.

FIG. 5 is a perspective view showing the configuration of an opticalfiber using a two-dimensional photonic crystal.

FIG. 6 is a schematic diagram showing the intensity of the electricfield of the first band propagation light in the Z-axis direction withinthe one-dimensional photonic crystal.

FIG. 7 is a schematic diagram showing the intensity of the electricfield of the higher-order band propagation light in the Z-axis directionwithin the one-dimensional photonic crystal.

FIG. 8 is a cross-sectional view showing the configuration of a photoniccrystal optical waveguide according to an embodiment of the presentinvention.

FIG. 9 is a diagram schematically showing the intensity in the Z-axisdirection of the electric field of the guided light in the photoniccrystal optical waveguide according to an embodiment of the presentinvention.

FIG. 10 is a schematic diagram showing the electric field of a photoniccrystal optical waveguide in accordance to another embodiment of thepresent invention.

FIG. 11 is a cross-sectional view of a photonic crystal opticalwaveguide in accordance with another embodiment of the presentinvention.

FIG. 12 is a cross-sectional view of a photonic crystal opticalwaveguide in accordance with another embodiment of the presentinvention.

FIGS. 13A and 13B show band diagrams of one-dimensional photoniccrystals in which two different alternating materials of the samethickness are stacked upon another.

FIGS. 14A and 14B are schematic diagrams of a two-dimensional photoniccrystal having a multilayer structure.

FIG. 15 is a perspective view of a photonic crystal optical waveguideaccording to an embodiment of the present invention.

FIG. 16 is a perspective view showing an optical waveguide elementcompensating a phase difference in accordance with an embodiment of thepresent invention.

FIG. 17 is a schematic diagram of a photonic crystal optical fiber inaccordance with an embodiment of the present invention.

FIG. 18 is a schematic diagram of a concentric circular photonic crystaloptical fiber in accordance with an embodiment of the present invention.

BEST MODE FOR CARRYING OUT THE INVENTION

A photonic crystal optical waveguide according to an embodiment of thepresent invention can propagate waves associated with specifichigher-order photonic bands. Thus, the function of the photonic crystalcan be utilized with high efficiency.

In a photonic crystal optical waveguide according to a preferredembodiment of the present invention, there is a photonic band in thepropagation direction of the light in the core, the incident-side phasemodulation portion phase-modulates incident guided light and lets itpropagate through the core of the optical waveguide portion, and thecore propagates all or at least half of the energy of thephase-modulated guided light as a wave associated with higher-orderphotonic bands of said photonic bands. Thus, higher-order bandpropagation light with little loss due to first-order band propagationlight can be caused to propagate through the core. Therefore, it ispossible to use the photonic crystal optical waveguide as a dispersioncompensation element or as an optical delay element, for example.

The incident-side phase modulation portion may be a phase grating havinga refractive index period that is adjusted to the refractive indexperiod of the core.

The incident-side phase modulation portion may be a phase grating havingthe same structure as the core, and having the same refractive indexperiod as the core.

Preferably, the incident-side phase modulation portion is a portionseparated by cutting an end portion vicinity on the incident surfaceside of the core. Thus, the incident-side phase modulation portion canbe fabricated easily.

Moreover, the core may let a wave associated with the second coupledphotonic band from the lowest order of the phase-modulated guided lightpropagate.

Also, it is preferable that the photonic crystal optical waveguidefurther comprises an emerging-side phase modulation portion arranged inclose proximity or in contact with an emerging surface of the core fromwhich the guided light emerges. Thus, the light emerging from the corecan be changed into a plane wave.

Also, the emerging-side phase modulation portion may have a structureconverting the light emerging from the emerging surface of the core intoa plane wave.

The emerging-side phase modulation portion may be a phase grating havinga refractive index period that is adjusted to the refractive indexperiod of the core.

The emerging-side phase modulation portion may be a phase grating havingthe same structure as the core, and having the same refractive indexperiod as the core.

Preferably, the emerging-side phase modulation portion is a portionseparated by cutting an end portion vicinity on the emerging surfaceside of the core. Thus, the emerging-side phase modulation portion canbe fabricated easily.

Also, it is preferable that the cladding is made of a photonic crystalhaving a periodic refractive index in at least one directionperpendicular to a propagation direction of the guided light and havinga uniform refractive index in the propagation direction of the guidedlight. Thus, leaking of the light from the core can be prevented evenwhen the effective refractive index of the core is low.

The core may comprise an active material having an optical non-lineareffect. Thus, it is possible to provide an optical element with a largenon-linear optical effect.

The core may be made of a multilayer film layer having a periodicrefractive index in one or two directions perpendicular to thepropagation direction of the guided light and having a uniformrefractive index in the propagation direction of the guided light.

Preferably, the optical waveguide portion has a fiber shape with asubstantially circular cross section, and the core is fiber-shaped withthe cladding formed around the core, and the core and the cladding havea uniform refractive index in the propagation direction of the guidedlight. Thus, it is possible to provide a fiber-shaped dispersioncompensation element or optical delay element, for example.

The refractive index periods of the core and the cladding may besymmetric with respect to the center axis of the optical waveguideportion, which is parallel to the propagation direction of the guidedlight.

Preferably, the optical waveguide portion comprises a fiber-shapedhomogenous substance with a substantially circular cross section, aplurality of cavities are formed in the homogenous substance along itslongitudinal direction, the plurality of cavities are formed symmetricto the center axis of the optical waveguide portion, which is parallelto the propagation direction of the guided light. Thus, it is possibleto provide a fiber-shaped dispersion compensation element or opticaldelay element, for example.

All or some of the cavities may be filled with a fluid substance. Thecavities may be filled with an acrylic monomer as the fluid substance,and irradiated with UV light from the outside to be polymerized intoacrylic polymer.

The refractive index in the cross section of the optical waveguideportion may change periodically and in concentric circles with respectto a distance from the center axis of the optical waveguide portion,which is parallel to the propagation direction of the guided light.

The following is a detailed explanation of embodiments of the presentinvention.

First, the propagation of light in a photonic crystal is explained. FIG.1 is a cross-sectional view showing a one-dimensional photonic crystal1. In FIG. 1, the Z-axis direction is the propagation direction of thelight, and the Y-axis direction is a direction perpendicular to thepropagation direction of the light. The one-dimensional photonic crystal1 has a refractive index periodicity only in the Y-axis direction. Morespecifically, a material 5 a and a material 5 b with differentrefractive indices are layered one upon the other in alternation in theY-axis direction, thus forming a multilayer structure 5. The refractiveindex is uniform in the propagation direction (Z-axis direction) of thelight. The thickness of the material 5 a is t_(A), and its refractiveindex is n_(A). Similarly, the thickness of the material 5 b is t_(B),and its refractive index is n_(B). Consequently, with these layered uponone another, the photonic crystal 1 has a multilayer structure with aperiod “a”. This period a is (t_(A)+t_(B)).

In FIG. 1, the one-dimensional photonic crystal 1 constitutes a core,and air is arranged around it as a cladding (not shown in the drawings),thus constituting an optical waveguide. When a plane wave with a vacuumwavelength of λ₀ is incident as incident light 2 from a side face 1 a ofthe one-dimensional photonic crystal 1 serving as the core, it ispropagated as guided light 4 through the material 5 a and the material 5b of the one-dimensional photonic crystal 1, and emerges as emergentlight 3 from the side face 1 b opposite from the side face 1 a. In thissituation, the manner in which the light propagates within theone-dimensional photonic crystal 1 can be determined by calculating andplotting the photonic bands. Methods of band calculation are describedin detail in “Photonic Crystals”, Princeton University Press (1995) andin Physical Review vol. B 44, No. 16, p. 8565, 1991, for example.

The photonic bands of the one-dimensional photonic crystal 1 shown inFIG. 1 are calculated by the above-mentioned band calculation. Thecalculation is performed under the assumption that the refractive indexperiodic structure continues infinitely in the Y-axis direction (thelayering direction) and that the layers extend infinitely in the X-axisand the Z-axis directions (the directions in which the layer surfacesextend).

FIG. 2 is a band graph showing the photonic band structure of the TEpolarized light in the one-dimensional photonic crystal 1 in FIG. 1.Moreover, FIG. 3 is a band graph showing the photonic band structure ofthe TM polarized light in the one-dimensional photonic crystal 1 inFIG. 1. It should be noted that the thickness t_(A) and the refractiveindex n_(A) of the material 5 a as well as the thickness t_(B) and therefractive index n_(B) of the material 5 b have the values noted below,where the thickness t_(A) and the thickness t_(B) are expressed in termsof the period a (a=t_(A)+t_(B)). n_(A) = 1.44, t_(A) = 0.5a n_(B) =2.18, t_(B) = 0.5a

In the multilayer structure 5 of the period a in which layers of thematerial 5 a and the material 5 b are layered in alternation, theresults of the band calculation for the first to third bands, calculatedby the plane wave method for the Z-axis direction (same for X-axisdirection), are shown in FIGS. 2 and 3. Here, TE polarized light is thepolarized light whose electric field points in the X-axis direction, andthe TM polarized light is the polarized light whose magnetic fieldpoints in the X-axis direction, The horizontal axes in FIGS. 2 and 3mark the size of the wave vector kz of the Z-axis direction in theone-dimensional photonic crystal 1, and the vertical axes mark thenormalized frequency. The normalized frequency is given as ωa/2πc, wherec is the angular frequency of the incident light, a is the period of themultilayer structure 5, and c is the speed of light in a vacuum. Thenormalized frequency can be expressed as a/λ₀, using the vacuumwavelength λ₀ of the incident light 2. In the following, the normalizedfrequency is expressed as a/λ₀, and it is also expressed this way inFIGS. 2 and 3. The one-dimensional photonic crystal 1 has no refractiveindex periodicity but a uniform refractive index in the Z-axisdirection, so that the horizontal axis in FIGS. 2 and 3 spreadsinfinitely without any Brillouin zone boundary.

In FIG. 1, if the vacuum wavelength of the incident light 2 is λ_(A),then there is a wave vector k_(A1) corresponding to the lowest-orderfirst band within the one-dimensional photonic crystal 1. In otherwords, the guided light 4 propagates in the Z-axis direction through thephotonic crystal optical waveguide 1 as a wave with the wavelengthλ_(A)=2π/k_(A1). The guided light 4 is in this case referred to as“first band propagation light” in the following.

Now, if incident light 2 with a vacuum wavelength of k_(B1) incident onthe one-dimensional photonic crystal 1, then there are wave vectorsk_(B1) and k_(B3) corresponding to the first and third bands. It shouldbe noted that the second band is “uncoupled” with respect to thepropagation in the Z-axis direction, so that it can be ignored.Consequently, a wave of first band propagation light with a wavelengthλ_(B1)=2π/k_(B1) and a wave of third band propagation light with awavelength λ_(B3)=2π/k_(B3) propagate in the Z-axis direction throughthe one-dimensional photonic crystal 1. Light of coupled bands that arenot the lowest-order band (first band), such as the third band light inFIG. 2, is generally referred to as “light propagated in higher-orderbands” in the following. Ordinarily, one of the second band and thethird band is coupled and the other one is uncoupled, and the first bandis coupled. A detailed explanation behind the theory of uncoupled bandscan be found in “Optical Properties of Photonic Crystals” by K. Sakoda,Springer-Verlag (2001).

The foregoing was an explanation of TE polarized light with reference toFIG. 2, but as can be seen from FIG. 3, also for TM polarized light therelation is similar to that for TE polarized light, so that furtherexplanations are omitted.

Here, the numeric value obtained by dividing the wavelength of light invacuum (λ_(A), λ_(B), etc.) by the corresponding wavelength in theone-dimensional photonic crystal (λ_(A1), λ_(B3), etc.) is defined asthe “effective refractive index.” As can be seen from FIG. 2 and FIG. 3,the normalized frequency a/λ₀ (vertical axis) and kz (horizontal axis)of the first band light are substantially proportiona, so that there issubstantially no change of effective refractive index with respect tochanges of the vacuum wavelength of the incident light. However, forlight propagated in higher-order bands, the effective refractive indexchanges considerably depending on the vacuum wavelength of the incidentlight, and the effective refractive index may drop below 1, as becomesclear from FIGS. 2 and 3.

It is well known that the value obtained by differentiating the bandcurves by kz (that is, the slope of the tangent at the band curves) inthe band diagrams shown in FIGS. 2 and 3 is the group velocity of theguided light 4. For higher-order bands of second and higher orders, theslope of the tangent becomes drastically smaller as the value of kzbecomes small, and at kz=0, the slope of the tangent becomes zero. Thisis due to group velocity anomalies, which is a characteristic phenomenonin photonic crystals. The group velocity anomalies in photonic crystalsare very large, and lead to a dispersion that is opposite to that inordinary homogenous materials. That is to say, in photonic crystals, asthe wavelength of the incident light becomes large, the group velocityslows down. Therefore, if an optical waveguide or an optical fiberutilizing light propagated in higher-order bands is made using aphotonic crystal, then it can be utilized as an optical delay element ora dispersion compensation element in optical communication.

FIG. 4 is a perspective view showing the configuration of a photoniccrystal optical waveguide 17, which is an optical waveguide elementusing the one-dimensional photonic crystal 15. The one-dimensionalphotonic crystal 15 is placed on a substrate 14, such that homogenousoptical waveguides 16 are placed at both ends of it and theone-dimensional photonic crystal 15 is sandwiched by these homogenousoptical waveguides 16. The one-dimensional photonic crystal 15 serves asthe core, whereas the cladding is provided by the surrounding air andthe substrate 14. The photonic crystal optical waveguide 17 shown inFIG. 4 is an optical waveguide element configured using theone-dimensional photonic crystal 15. It should be noted that in FIG. 4,the direction in which the light propagates is the Z-axis direction.

Incident light 12 is incident on one end of the photonic crystal opticalwaveguide 17. The incident light 12 is coupled into the homogenousoptical waveguide 16, and is coupled from the homogenous opticalwaveguide 16 into the one-dimensional photonic crystal 15. The lightpropagates in the longitudinal direction (Z-axis direction), and emergesas emitted light 13 from the other end of the photonic crystal opticalwaveguide 17. When this light is higher-order band propagation light,then a group velocity anomaly of this higher-order band propagationlight occurs in the one-dimensional photonic crystal 15. Thus, thephotonic crystal optical waveguide 17 can be used as an optical delayelement, for example.

FIG. 5 is a perspective view showing the configuration of an opticalfiber 21 using a two-dimensional photonic crystal. The optical fiber 21has a columnar shape, and light is propagated in its axial direction.The optical fiber 21 is provided with a core 22 and a cladding 23 thatis formed around the core 22. The core 22 is the two-dimensionalphotonic crystal having a uniform refractive index in the propagationdirection of the light (in Z-axis direction), and a refractive indexperiodicity in the X-axis and the Y-axis direction. The cladding 23 isnot made of a photonic crystal, but of an ordinary homogenous material.In the optical fiber 21 with this configuration, a similar band diagramas for the above-described one-dimensional photonic crystal is given forthe propagation of light in the direction in which the core 22, which isa two-dimensional photonic crystal, has a uniform refractive index.Consequently, if higher-order band propagation light is propagatedthrough the core 22 configured by this two-dimensional photonic crystal,then the optical fiber 21 can be used as an optical fiber attaining astrong dispersion compensation effect, for example.

However, there are a number of problems in using the photonic crystaloptical waveguide 17 or the optical fiber 21 shown in FIGS. 4 and 5 asan optical waveguide or an optical fiber for higher-order bandpropagation light. As becomes clear from FIGS. 2 and 3, if higher-orderband propagation light is propagated, first band propagation light isalways propagated as well. The first band propagation light causes aloss of energy when trying to utilize the higher-order band propagationlight, and leads to a considerable drop in the utilization efficiency ofthe incident light. Moreover, the first band propagation light has adifferent group velocity than the light propagated in higher-orderbands, so that there is the problem that signals are subjected to alarge wavelength dispersion.

Moreover, in FIG. 1, a refractive index structure that is periodic inthe Y-axis direction and the X-axis direction is exposed at the end face1 b at which the light emerges from the one-dimensional photonic crystal1. Therefore, also the higher-order band propagation light itself isperiodic in intensity and phase, so that the emitted light 3 is mixedwith diffraction light of various orders and directions. Consequently,it is difficult to handle the emitted light 3.

Furthermore, when the effective refractive index of the higher-orderband propagation light becomes smaller than the refractive index of thesurrounding medium (cladding) in contact with the one-dimensionalphotonic crystal 1, then the guided light 4 leaks out into the cladding.Thus, light may not be guided in the one-dimensional photonic crystal 1at the core. In particular when the effective refractive index of thehigher-order band propagation light is less than 1, there is the problemthat it is not possible to prevent the leaking of light, even when thecladding is air.

FIGS. 6 and 7 show the intensity of the electric field in the Z-axisdirection of the guided light 4 in the one-dimensional photonic crystal1 for the case that a plane wave is incident on the core from the endface 1 a of the one-dimensional photonic crystal 1 in FIG. 1. FIG. 6 isa schematic diagram showing the intensity of the electric field of thefirst band propagation light in the Z-axis direction within theone-dimensional photonic crystal 1 shown in FIG. 1. FIG. 7 is aschematic diagram showing the intensity of the electric field of thehigher-order band propagation light in the Z-axis direction within theone-dimensional photonic crystal 1 shown in FIG. 1. The electric fieldof the light is depicted in the form of waves. The wave crests 4a of theelectric field are shown as solid lines, and the wave troughs 4 b of theelectric field are shown as dashed lines. Moreover, the size of theamplitude is expressed by the thickness of those lines, and a thickerline represents a larger amplitude. It should be noted that thewavelength of the guided light is λ.

As shown in FIG. 6, even though the electric field amplitude of thefirst band propagation light in the material 5 a differs from that inthe material 5 b, the wave crests 4 a and the wave troughs 4 b of theelectric field form planes perpendicular to the Z-axis direction, sothat a propagation that is close to a plane wave is attained.

By comparison, in the higher-order band propagation light, “nodes 4 c”at which the electric field amplitude becomes zero occur near theboundary of the material 5 a and the material 5 b, as shown in FIG. 7.Therefore, one period of the layered structure formed by the adjacentmaterial 5 a and material 5 b is partitioned into two regions with awave crest and a wave trough. Since the phases of the waves are shiftedby half a wavelength at the adjacent regions (material 5 a and material5 b), the wave crests and wave troughs are out of synch. It is in thesecond and the third band that these two nodes 4 c per period occur. Forthe guided light in the higher-order bands, the number of nodes perperiod increases even more, and shifts by half a wavelength occurseveral times per period.

Consequently, for incident light of a wavelength at which a plurality ofbands contribute, there are a plurality of propagated light modes, whichoverlap and form a complex electric field pattern. For example, with theincident light with a vacuum wavelength of k_(B) shown in FIG. 2 thereis propagation light for the first band and the third band, so thatthere are a plurality of propagated light modes in the photonic crystal.Therefore, a complex propagation pattern results.

However, research by the inventors has shown that when incident lightthat has been subjected to a phase modulation is coupled into a photoniccrystal with photonic bands in the propagation direction of the guidedlight, then it is possible to propagate only certain higher-order bandpropagation light. The photonic crystal optical waveguides according toembodiments of the present invention utilize this.

Referring to the drawings, the following is an explanation of photoniccrystal optical waveguides according to embodiments of the presentinvention. FIG. 8 is a cross-sectional view showing the configuration ofa photonic crystal optical waveguide 10 according to the presentembodiment. As shown in FIG. 8, the photonic crystal optical waveguide10 is provided with an optical waveguide portion and a phase grating 6,which is a phase modulation portion. The optical waveguide portionincludes a core and a cladding. The core is constituted by aone-dimensional photonic crystal 1 having a refractive index structurethat is periodic only in the Y-axis direction. The cladding isconstituted by the air surrounding the core. In FIG. 8, the cladding isthe air around the one-dimensional photonic crystal 1 serving as thecore, so that it is not shown in the drawings. It should be noted thatthe cladding does not have to be air, and that it is also possible totake a suitable material as the cladding and arrange it around theone-dimensional photonic crystal 1.

The one-dimensional photonic crystal 1 is the same as the one shown inFIG. 1. That is to say, it has a multilayer structure 5, in which amaterial 5 a and a material 5 b with different refractive indices arelayered in alternation in the Y-axis direction. In the Z-axis direction,which is the direction in which the light is propagated, the refractiveindex is uniform. The period “a” of the multilayer structure 5 is thesum of the thickness of the material 5 a and the thickness of thematerial 5 b. Moreover, the one-dimensional photonic crystal hasphotonic bands in the direction in which the guided light is propagated(the Z-axis direction). It should be noted that in the followingdiagrams, the Z-axis direction is the propagation direction of thelight, and the Y-axis is the layering direction of the one-dimensionalphotonic crystal.

The phase grating 6 is arranged in close proximity or in contact with anend face of the one-dimensional photonic crystal 1 on which the light isincident. It is also possible that a space 18 is formed between thephase grating 6 and the one-dimensional photonic crystal 1, for example.

FIG. 9 is a diagram schematically showing the intensity of the electricfield in the Z-axis direction of the guided light in the photoniccrystal optical waveguide 10 of the present embodiment. In FIG. 9, theelectric field of the light is depicted in the form of waves, and thewave crests 4 a of the electric field are shown as solid lines, whereasthe wave troughs 4 b of the electric field are shown as dashed lines.Moreover, the size of the amplitude is expressed by the thickness ofthose lines, and a thicker line represents a larger amplitude.

The effect that the phase grating 6 has on the incident light (planewave) is to cause a difference of about half a wavelength in the perioda in the Y-axis direction. When the incident light 7, which is a planewave, is incident on the phase grating 6, then an electric field patternthat is similar to the higher-order band propagation light in theone-dimensional photonic crystal shown in FIG. 7 forms in the space 18.The inventors found by simulation that when the light 8 having thiselectric field pattern is incident from the end face of theone-dimensional photonic crystal 1 and is transmitted inside theone-dimensional photonic crystal 1, then there is no light propagated inthe first band, and only higher-order band propagation light ispropagated. Thus, all or more than half of the energy of the wavepropagated inside the one-dimensional photonic crystal 1 can beassociated with the higher-order photonic bands.

This means that when a suitable phase-modulated wave having the sameperiod in the same direction as the periodic structure of the photoniccrystal is coupled into that photonic crystal, then it is possible toattain a propagation of light in specific bands only.

A phase grating 6 is used as the phase modulation portion, and thefollowing is a more specific explanation of the parameters for the phasemodulation portion.

The simplest phase modulation portion is a phase grating having the sameperiod as the periodic multilayer films of the core constituted by theone-dimensional photonic crystal 1. The phase grating 6 can beconfigured by layering a material 5 c and a material 5 d with differentrefractive indices periodically in alternation, as shown in FIG. 8. Theinventors found by simulation that it is preferable to optimize thephase grating 6.

For example, it is preferable to optimize the thicknesses t_(C) andt_(D) in the Y-axis direction of the material 5 c and the material 5 din FIG. 8, the length L in the propagation direction (Z-axis direction)of the light of the phase grating 6, the thickness G in the Z-axisdirection of the space 18, and the refractive index n_(G) of the space18. For the optimization of these, it is preferable to adjust, forexample, the ratio between the thicknesses t_(A) and t_(B) of thematerials 5 a and 5 b, which are characteristic for the multilayerstructure 5 of the one-dimensional photonic crystal 1, or the refractiveindices of the material 5 a and the material 5 b. It is preferable tosynchronize the periods of the phase grating 6 and the one-dimensionalphotonic crystal 1. More specifically, it is preferable that theconditiont _(A) +t _(B) =t _(C) +t _(D)is satisfied, and that the center in the Y-axis direction of thematerial 5 a and the material 5 c matches the center in the Y-axisdirection of the material 5 b and the material 5 d, respectively. Thus,the periods of the phase grating 6 and the one-dimensional photoniccrystal 1 are synchronized to be the same.

It is preferable that also the thickness G of the space 18 between thephase grating 6 and the one-dimensional photonic crystal 1 is chosen tobe in a suitable range, because it affects the guided light.

Moreover, if the period a (=t_(A)+t_(B)) of the multilayer structure 5is not greater than the vacuum wavelength λ₀ of the incident light 7,and an air layer is taken as the space 18 in the gap between the two,then the ±1-order diffraction light due to the phase grating 6 cannotpropagate and the reflection light increases. One way to prevent this isto fill the space 18 with a medium with a large refractive index so asto increase the refractive index of the space 18. More specifically, amedium with a refractive index n_(G) should be filled into the space 18,where n_(G) is given by the following equation:λ₀/n_(G)<aHere, if the condition λ₀/n_(G)<a is given, then it is preferable thatthe thickness G of the space 18 is not more than up to 5 times thewavelength (λ₀/n_(G)) within the medium. When the thickness G is toolarge, then the ±1-order diffraction light and the -1-order diffractionlight become too far away from one another, and the portion whereinterference waves are formed diminishes.

Even when the condition λ₀/n_(G)<a is given, if the thickness G of thespace 18 is almost zero (a tenth of λ₀/n_(G) or less), then there arecases in which coupling of evanescent waves becomes possible.

It is also possible to form the phase grating 6 by cutting theone-dimensional photonic crystal 1 near the end face 1 a on the incidentside and separating it from the one-dimensional photonic crystal 1. Thegroove formed by this cutting between the one-dimensional photoniccrystal 1 and the phase grating 6 thus becomes the space 18. In thiscase, adjusting the thickness of the cut portion (the thickness L of thephase grating 6) and the width of the groove (width G of the space 18)can ensure that only certain higher-order band propagation light ispropagated. Needless to say, the groove may be an air layer, or it maybe filled with a homogenous medium.

Furthermore, FIG. 10 is a schematic diagram showing the electric fieldof a photonic crystal optical waveguide 20 in accordance with anotherembodiment of the present invention. FIG. 10 shows a configuration ofthe photonic crystal optical waveguide 10 in FIG. 9, in which a phasegrating 6 b serving as a phase modulation portion that is similar to theabove-described phase grating 6 arranged at the end face on the incidentside is arranged in close proximity or in contact with the emerging sideof the one-dimensional photonic crystal 1. A space is formed between thephase grating 6 b and the one-dimensional photonic crystal 1. Thus, theemerging light 8 b associated with specific bands that is emitted fromthe one-dimensional photonic crystal 1, is converted into a plane wave9. That is to say, the emerging light 8 b associated with specific bandsthat is emitted from the one-dimensional photonic crystal 1 is convertedinto a plane wave when it is incident on the phase grating 6 b. Itshould be noted that in FIG. 10, only the portions of the wave crests 4a of the electric field are shown. It is preferable that the structureof the phase grating 6 b is similar to that of the phase grating 6 inFIG. 8, and it is also preferable that the space between the photoniccrystal 1 and the phase grating 6 b is set in accordance with similarconditions as the space 18 in FIG. 8.

It is possible to attain a similar effect as with the above-describedphotonic crystal optical waveguides by taking the optical fiber 21 witha two-dimensional photonic crystal shown in FIG. 5 as the opticalwaveguide portion and placing phase modulation portions such as thephase gratings at both ends. In this case, the phase grating also shouldhave a two-dimensional structure, similar to the optical fiber 21serving as the optical waveguide portion. Thus, it is possible torealize propagation of only specific higher-order band propagationlight, similar as with a one-dimensional photonic crystal.

Also in this case, when the effective refractive index of thehigher-order band propagation light becomes smaller than the refractiveindex of the cladding 23 formed around the core 22, then propagatedlight may leak due to refraction from the core 22. In particular whenthe effective refractive index of the higher-order band propagationlight is not greater than 1, it is not possible to prevent the leakageof light when the cladding is air.

In order to prevent the leakage of guided light from the core due to alowering of the effective refractive index and to confine the guidedlight in the core, it is preferable to provide a reflective layer 32,such as a metal film, as a cladding around the core made of the photoniccrystal, as shown in FIG. 11 for example. FIG. 11 is a cross-sectionalview of a photonic crystal optical waveguide 30 in accordance withanother embodiment of the present invention. The photonic crystaloptical waveguide 30 in FIG. 11 is provided with a core made of theone-dimensional photonic crystal 1 shown in FIG. 1, and phase gratings36 arranged at the two end faces and separated from the core by spaces38. Reflective layers 32, made of a metal film or the like, serving asthe cladding are formed in contact with the one-dimensional photoniccrystal 1, sandwiching the same. With this configuration, light leakingfrom the one-dimensional photonic crystal 1 serving as the core isreflected by the reflective layer 32 and is confined in theone-dimensional photonic crystal 1 serving as the core.

However, when reflective layers 32 are used for the cladding, problemsmay occur, such as a lowering of the strength of the photonic crystaloptical waveguide 30 serving as the multilayer structure or attenuationdue to insufficient reflectance at the reflective layers 32. FIG. 12 isa cross-sectional view of a photonic crystal optical waveguide 40 inaccordance with another embodiment of the present invention. Thephotonic crystal optical waveguide 40 shown in FIG. 12 differs from thephotonic crystal optical waveguide 30 shown in FIG. 11 in that not areflective film, but a photonic crystal 11 is used for the cladding. Asshown in FIG. 12, the photonic crystal optical waveguide 40 is providedwith the photonic crystal 11 having a periodic refractive index as thecladding, instead of the reflective film. The photonic crystal 11serving as the cladding has a refractive index periodicity in at leastone direction perpendicular to the propagation direction of the guidedlight (Z-axis direction) and has a uniform refractive index in thedirection in which the guided light is propagated. It should be notedthat the structure of the photonic crystal 11 serving as the cladding isdifferent from that of the one-dimensional photonic crystal 1 serving asthe core, and also has a different refractive index period. Thus, thephotonic band gaps of the photonic crystal 11 serving as the claddingare set to locations corresponding to the wave vector kz in the Z-axisdirection of the propagation light of the one-dimensional photoniccrystal 1 serving as the core. Therefore, a confinement of the guidedlight to the one-dimensional photonic crystal 1 can be realized.

The following is an explanation of preferable conditions for the casethat a photonic crystal 11 is used for the cladding. FIGS. 13A and 13Bare band diagrams of one-dimensional photonic crystals in which twodifferent materials of the same thickness are stacked upon another inalternation. The refractive indices of these two materials are 1.00 and1.44, respectively. The period of the multilayer structure in FIG. 13Ais set to a, and the period of the multilayer structure of the two typesin FIG. 13B is set to a′=0.434a. FIGS. 13A and 13B are both showntwo-dimensionally on the same scale. The vertical direction correspondsto the Y-axis direction, and the first Brillouin zones are shown, bandfor band in the vertical direction, within the range of ±π/a and ±π/a′from the center. Moreover, the horizontal direction corresponds to theZ-axis direction (same as the X-axis direction), and there are noboundary lines of Brillouin zones, because there is no periodicity ofthe refractive index in this direction. The range for which thecalculation was performed is shown to the left and the right in thefigure, but there is no particular significance to this range.

The positions within the Brillouin zones signify the wave vector withinthe photonic crystal, and the contour lines signify bands correspondingto specific normalized frequencies a/λ₀ (or a′/λ₀). Incidentally, FIGS.2 and 3 discussed above are one-dimensional representations for only aportion of such band diagrams (namely for the portion in positive Z-axisdirection).

FIG. 13A shows bands corresponding to the wavelength λ₀=0.725a(a/λ₀=1.38) with bold lines, for a one-dimensional photonic crystal withperiod a. Also, the wave vector representing the first band propagationlight in the Z-axis direction is represented by a dashed arrow 41,whereas the wave vector representing the higher-order band propagationlight in the Z-axis direction is represented by an arrow 42. Also, FIG.13B shows the bands corresponding to the same wavelength (λ₀=0.725a(a′/λ₀=0.60) with a bold line.

A dashed line 43 indicating the size of the arrow 42 representing thewave vector of the higher-order band propagation light and a dashed line44 indicating the size of the dashed arrow 41 representing the wavevector of the first band propagation light are drawn to FIG. 13B. As canbe seen from these drawings, there are no corresponding bands in FIG.13B. In FIG. 13B, there are no bands corresponding to the wave vectorsof the higher-order band propagation light in FIG. 13A (same as for theZ components). Consequently, the higher-order propagation bands in thecrystal of the period a shown in FIG. 13A do not exist in the photoniccrystal of the period a′ shown in FIG. 13B.

Therefore, the optical waveguide portion may be configured taking aone-dimensional photonic crystal 1 with the period a as the core andarranging a photonic crystal 11 with a period a′ on both sides thereofas the cladding, as shown in FIG. 12. In such an optical waveguideportion, the higher-order band propagation light that is propagated inthe photonic crystal of period a cannot leak out to the photonic crystalof period a′. Consequently, it is possible to confine and propagate thelight in the core constituted by the photonic crystal of period a.

The material and the structure of the photonic crystal 11 used for thecladding may differ from that of the one-dimensional photonic crystal 1used for the core. However, in view of the effort involved infabricating the multilayer structure, it is preferable to use the samematerial for both, and to make the refractive index period of thephotonic crystal 11 used for the cladding smaller. Needless to say, itis necessary to design the photonic crystal optical waveguide afterconfirming by band calculation that the wave vectors in the core do notexist in the cladding.

It should be noted that according to FIGS. 13A and 13B, a bandcorresponding to the first band propagation light does not exist in FIG.13B, so that also the first band propagation light is propagated in theone-dimensional photonic crystal 1. However, if the period a′ of thephotonic crystal 11 of the cladding or the structure of the multilayerfilm is adjusted, then the first band propagation light can be caused toleak from the one-dimensional photonic crystal 1 serving as the core,and the higher-order band propagation light can be confined. Bydesigning such conditions through a band calculation, it is possible toachieve a photonic crystal optical waveguide in which light propagatedin the first band can be completely purged midway.

Ordinarily, to determine the confinement with a band diagram, a photoniccrystal with an infinite periodic structure is assumed. Therefore, ifthe confining photonic crystal has only for example three periods inpractice, then the confinement may become insufficient, and the guidedlight leak to the outside. Needless to say, providing an unnecessarilylarge number of periods is undesirable with regard to cost as well asdurability and precision of the multilayer film. In practice, it ispreferable to determine the number of periods that is necessary at aminimum experimentally or through electromagnetic simulation.

The cases described so far related to confining higher-order bandpropagation light in a one-dimensional photonic crystal. Also in thecase of two-dimensional photonic crystal optical fibers, it is possibleto realize a confinement by enclosing the core portions with photoniccrystals for cladding.

FIGS. 14A and 14B schematically show a two-dimensional photonic crystalserving as the multilayer structure. FIGS. 14A and 14B are examples oftwo-dimensional photonic crystals having a periodicity in both theX-axis direction and the Y-axis direction and no periodicity in theZ-axis direction. In the photonic crystal 50 a in FIG. 14A, four typesof media 51, 52, 53 and 54 are layered. These four types of media 51,52, 53 and 54 are exposed at the XY cross section. The photonic crystal50 b of FIG. 14B is made of three types of media 55, 56 and 57. Thephotonic crystal 50 b can be made easily by first layering two types ofmedia 55 and 56 in the Y-axis direction, and then forming grooves thatare parallel to the YZ plane periodically in the X-axis direction. Inthis case, the medium 57 is air, but it is also possible to fill thegrooves with a medium other than air.

It is also possible to realize a photonic crystal optical waveguideaccording to an embodiment of the present invention by using thesephotonic crystals 50 a and 50 b for at least one of the core, thecladding and the phase grating.

The following is a more detailed explanation of the conditions to besatisfied by the present embodiment.

Although not shown in FIG. 9, the higher-order bands of the fourth bandand above also show a similarly large wavelength dispersion as thesecond and third bands. However, towards higher orders of the bandspropagating light, the number of nodes of the wave that are present perperiod in Y-axis direction increases, so that the pattern of the phasemodulation becomes more complicated. Consequently, it is most desirableto use the second or the third band, in which there are two nodes perperiod, as the higher-order propagation band. Needless to say, it is notpossible to utilize the “uncoupled” bands, so that the preferable bandis the second coupled band counted from the lowest order. As notedabove, the first band is coupled.

Moreover, a so-called “photonic crystal group velocity anomaly” occursin the light propagated in the higher-order propagation bands, so thatan increased non-linear effect can be expected. In the presentembodiment, no energy is taken up by the first band light in which thereis substantially no group velocity anomaly, so that it is possible toattain an increased effect of optical non-linearities by includingnon-linear optical material in the core portion of the multilayer filmor the photonic crystal optical fiber. (See Optical Fiber Communication2002/Conference and Exhibit Technical Digest ThK4 (p. 468))

For example, in the one-dimensional photonic crystal 15 serving as thecore, as shown in FIG. 4, there is a large difference between thestructure in the X-axis direction and in the Y-axis direction.Therefore, the effective refractive index and the group velocity differdepending on the polarization direction. This is clear from the factthat the characteristics in FIG. 2 (TE polarized light) differ fromthose in FIG. 3 (TM polarized light). Consequently, in the photoniccrystal optical waveguides according to the present embodiment, it ispreferable to insert a corrective birefringent element into the lightpath, in order to eradicate the difference between the polarizationmodes of the optical waveguide portion. It should be noted that it ispossible to use, for example, a birefringent crystal, a structuralbirefringent element or a photonic crystal as the birefringent element.

As for the material of the photonic crystal used in the presentembodiment, there is no particular limitation as long as itstransparency can be ensured in the wavelength range used. Suitablematerials for the one-dimensional case are silica, silicon nitride,silicon, titanium oxide, tantalum oxide, niobium oxide and magnesiumfluoride, which are ordinarily used as the material for multilayer filmsand which have excellent durability and film-manufacturing costs. Withthese materials, a multilayer film structure can be formed easily bywell-known methods, such as sputtering, vacuum deposition, ion assisteddeposition or plasma CVD, for example. In the case of a two-dimensionalphotonic crystal fiber, the simplest configuration is one with air holesarranged in a quartz fiber.

As the ratio of the refractive indices between the materialsconstituting the photonic crystal becomes large, also the wavelengthdispersion, for example, tends to increase. Consequently, it ispreferable that the photonic crystal is constituted by a combination ofhigh refractive index and low refractive index materials, forapplications in which such characteristics are necessary. As forrefractive index ratios that can be used in practice, when air, whichhas a refractive index of 1, is used as the low refractive indexmaterial and InSb, which has a refractive index of 4.21, is used as thehigh refractive index material, then a refractive index ratio greaterthan 4 can be attained (see “BISHOKOGAKU HANDBOOK” (MicroopticsHandbook), p. 224, Asakura Shoten, 1995) When the refractive index ratioof the materials constituting the photonic crystal becomes small, thenthe difference in the characteristics depending on the polarizationdirection tends to become small, so that it is advantageous to combinematerials with a small refractive index ratio to realize non-dependencyon polarization. However, when the refractive index ratio becomes verysmall, then the modulation effect becomes weak and the expected effectsmay not be attained, so that it is preferable to ensure a refractiveindex ratio of at least 1.2.

The space by which the optical waveguide portion and the phase gratingportion are separated can be formed by first layering a multilayeredfilm and fabricating a multilayer structure, and then successivelyperforming the ordinary steps of applying a resist layer, patterning,etching and removing the resist layer. The groove portion shown in FIG.8 (the space 18) may be filled with air, or it may be a vacuum. Thus,the space 18 will have a low refractive index. It is also possible tofill a medium into the space 18. As the medium filled into the space 18,it is possible to use an organic resin, glass in a sol state, or amolten semiconductor material or the like. It should be noted thatsol-state glass can be turned into transparent glass by heating it afterturning it into a gel.

By selecting suitable materials, it is possible to use the photoniccrystal optical waveguide of the present embodiment for light of atypically used wavelength range of about 200 nm to 20 μm, and to attainsatisfactory characteristics. Moreover, the present embodiment has beenexplained for light, but it can be applied not only for light but forelectromagnetic radiation in general.

It should be noted that this is also the same for the space between thephotonic crystal and the phase modulation portion if a phase modulationportion is arranged on the side of the emergent end of the photoniccrystal.

FIG. 15 is a perspective view of a photonic crystal optical waveguideaccording to an embodiment of the present invention.

The photonic crystal optical waveguide 69 has a substrate 61. aone-dimensional photonic crystal 66 serving as the core arranged on thesubstrate 61, and a phase grating 66 a and a phase grating 66 b arrangedat the end faces on the incident side and the emergent side of theone-dimensional photonic crystal 66, with a space 68 a and a space 68 barranged between the one-dimensional photonic crystal 66 and the phasegrating 66 a and the phase grating 66 b. It should be noted that inpractice, reflective layers (see FIG. 11 or FIG. 12) of a metal film ora one-dimensional photonic crystal are disposed above and below theone-dimensional photonic crystal 66, but this is not shown in thefigure. Moreover, a homogenous optical waveguide 67 a made of ahomogenous material is placed on the outer side of the phase grating 66a. A birefringent element 64 and a homogenous optical waveguide 67 b areplaced on the outer side of the phase grating 66 b. It should be noticedthat the cladding is given by the air around the one-dimensionalphotonic crystal 66. Moreover, the phase grating 66 a and the phasegrating 66 b were originally the end portions of the one-dimensionalphotonic crystal 66, and are made by cutting and separating the endportions of the one-dimensional photonic crystal 66.

The one-dimensional photonic crystal 66 can be fabricated, for example,by forming a periodic multilayer film on the entire surface of thesubstrate 61, and then etching away all of the multilayer film exceptfor a line-shaped portion. It should be noted that the one-dimensionalphotonic crystal 66 has a uniform refractive index in the direction inwhich the light propagates, and has a periodic refractive index in thelayering direction.

The incident light 62 (signal light) is coupled from an optical fiber orthe like into the homogenous optical waveguide 67 a. This signal lightpropagates through the homogenous optical waveguide 67 a, passes throughthe phase grating 66 a and is fed to the one-dimensional photoniccrystal 66. A space 68 a is formed between the phase grating 66 a andthe one-dimensional photonic crystal 66. As described above, the signallight is incident on the one-dimensional photonic crystal 66 serving asthe core after passing through the phase grating 66 a, so that theguided light propagating through the one-dimensional photonic crystal 66is only higher-order band propagation light.

The higher-order band propagation light that is propagated through theone-dimensional photonic crystal 66 emerges from the emerging face ofthe one-dimensional photonic crystal 66 into the space 68 b, is incidenton the phase grating 66 b and is again converted into a plane wave bythe phase grating 66 b. The light that has been converted into a planewave is fed from the phase grating 66 b to the birefringent element 64,the phase shifts due to the polarization modes are compensated, and thelight is fed into the homogenous optical waveguide 67 b. The emerginglight 63 that emerges after passing through the homogenous opticalwaveguide 67 b is then coupled into an optical fiber, for example.

As noted above, the group velocity of the higher-order band propagationlight changes considerably depending on the wavelength of the incidentlight, so that this photonic crystal optical waveguide 69 can be usedfor applications such as dispersion compensation elements or opticaldelay elements of signal light for optical communication. Moreover,propagated light with slow group velocity increases the non-linearoptical effects, as noted above. The following lists a number of ways inwhich it can be used as an element with a much larger non-linear opticaleffect than in conventional elements. For example, it is possible toincrease the non-linear optical effect by doping the portion of theone-dimensional photonic crystal 66 with microscopic particles of asubstance having a non-linear optical effect. More specifically, it ispossible to disperse microscopic particles and use the effect of quantumdots.

As another method, it is possible to increase the non-linear opticaleffect by placing a thin-film layer including a substance exhibiting anon-linear optical effect at every single period of the one-dimensionalphotonic crystal 66. More specifically, it is possible to fabricate atleast one side of the thin-film layers by a sol-gel method, and to letthem include an organic pigment or an organic substance withphotorefractivity.

Another method is to increase the non-linear optical effect by taking amaterial with non-linear effect for the material from which theone-dimensional photonic crystal 66 is made. More specifically, thematerial of the one-dimensional photonic crystal may be a substance withlarge non-linearity, such as LiNbO₃ or the like.

FIG. 16 is a perspective view showing an optical waveguide element 70compensating a polarization-dependent phase difference. In FIG. 16, twoof the photonic crystal optical waveguides 69 shown in FIG. 15 are used.One of the photonic crystal optical waveguides 69 is rotated relative tothe other by 90° around the propagation direction of the light, andconnected to it. It should be noted that the homogeneous waveguide onthe emerging side of the photonic crystal optical waveguide 69 placed atthe incident side (on the left in FIG. 16) and the homogeneous waveguideon the incident side of the photonic crystal optical waveguide 69 placedat the emerging side (on the right in FIG. 16) may be omitted, as shownin FIG. 16. Moreover, also the birefringent element that was used inFIG. 15 is omitted. The two one-dimensional photonic crystal opticalwaveguides 69 are connected by the phase grating 66 b on the emergingside and the phase grating 66 a on the incident side.

The TE polarization components and the TM polarization components of theplane wave incident on the photonic crystal optical waveguide 69 on theincident side have different group velocities and wavelengths in thewaveguide, so that there is a phase difference, an intensity difference,and a difference in the non-linear effect. However, by letting the wavepass through the photonic crystal optical waveguide 69 on the emergingside, which has the same structure and length as the photonic crystaloptical waveguide 69 on the incident side and is only rotated by 90°relative to it, the phase difference, the intensity difference, and thedifference in the non-linear effect are canceled. Consequently, thereare no polarization-dependent differences in the optical waveguideelement 70 in FIG. 16.

Instead of the one-dimensional photonic crystal 66 shown in FIG. 15, itis also possible to use a two-dimensional photonic crystal that isperiodic in both the Y-axis direction and the X-axis direction, as shownin FIGS. 14A and 14B, for example. In this case, it is possible toeliminate polarization mode dependent differences by optimizing thestructure. Needless to say, in this case, also the phase gratingsfabricated by cutting the two-dimensional photonic crystal serving asthe core have a two-dimensional structure.

It should be noted that, as shown in FIG. 14B, making the photoniccrystal two-dimensional can be easily achieved by forming groovesparallel to the Z-axis direction by means of etching the layers of amultilayer film.

FIG. 17 is a schematic diagram of a photonic crystal optical fiber inaccordance with an embodiment of the present invention.

The optical fiber 79 serving as the optical waveguide portion of thephotonic crystal optical waveguide is made of a core 71 having atwo-dimensional photonic crystal structure, and a cladding 72 formedaround that. It should be noted that the refractive index is uniform inthe direction in which light is propagated. Phase lattices 76 a and 76 bmatching the period of the core 71 are placed at the two ends of theoptical fiber 79. The incident light (plane wave, not shown in thedrawings) propagates through the core 71 as higher-order bandpropagation light, and is restored to a plane wave on the emerging side.The lattice elements on both sides are the same, so that the opticalfiber can be used in both directions.

It should be noted that it is preferable that the refractive indexperiod of the core 71 and the cladding 72 is symmetric with respect tothe center axis of the optical fiber 79. This has the advantage thatpolarization mode dependent differences do not occur.

The photonic crystal of the cladding 72 of the optical fiber 79 has aperiod and a structure that are different from the photonic crystal ofthe core 71, and serves the role of confining the guided light in thecore 71 through photonic band gaps. It should be noted that it issufficient if the cladding 72, which is made of a photonic crystal, hasa thickness at which the light is confined in the core 71, and it is notnecessary to form the photonic crystal all the way to the outercircumference of the optical fiber 79.

The light guided by the optical fiber 79 is higher-order band light, sothat there is a much greater group velocity anomaly than withconventional optical fibers using single mode propagation with thelowest order band. Consequently, it is possible to attain a strongdispersion compensation effect and non-linear optical effect.

Moreover, the core 71 has a periodic structure and its size is notlimited, so that it is easy to realize a core 71 with a large diameter,and the connection of fibers can be simplified.

FIG. 18 is a schematic diagram of a concentric circular photonic crystaloptical fiber 89 in accordance with an embodiment of the presentinvention.

The optical fiber 89 has a periodic refractive index distribution in theradial direction. The optical fiber 89 is constituted by a core 81 and acladding 82 which are made of a two-dimensional photonic crystal havinga periodic and concentric circular refractive index period with respectto the distance from the center axis. It should be noted that therefractive index is uniform in the direction in which light ispropagated. Phase lattices 86 a and 86 b matching the period of the core81 are placed at the two ends of the optical fiber 89. The incidentlight (not shown in the drawings), which is a plane wave, propagatesthrough the core 81 as higher-order band propagation light, and is againrestored to a plane wave on the emerging side. The phase gratings 86 aand 86 b on both sides are the same, so that the incident and theemerging directions also can be reversed.

The cladding 82 has a refractive index period that is different fromthat of the core 81, and serves the role of confining the guided lightin the core 81 through photonic band gaps.

The optical fiber 89 is symmetric with respect to the optical axis, sothat there is the advantage that there are no polarization modedependent differences. The effect due to the group velocity anomaliesand the fact that there are no restrictions regarding the size of thecore portion are the same as in the optical fiber 79 of FIG. 17.

Also, the optical fibers 79 and 89 in FIGS. 17 and 18 can be fabricatedby forming cavities in a fiber-shaped homogenous material having asubstantially circular cross section and forming a periodic refractiveindex with the homogenous material and air. It should be noted that aplurality of cavities should be formed along the longitudinal directionof the fiber-shaped homogenous material. The cavities should be parallelto the guided light. It is furthermore possible to fill a fluidsubstance into all or some of the cavities, and to form differentrefractive index periods. For example, it is possible to fill acrylicmonomers as the fluid substance, irradiate UV light from outside, andpolymerize the acrylic monomers.

It should be noted that the configurations shown in detail in theforegoing embodiments are mere examples, and that the present inventionis not limited by these specific examples. For example, the photoniccrystal serving as the core of the optical waveguide of the presentembodiments has a refractive index that is uniform in the direction inwhich light is propagated, and has a periodic refractive index in atleast one direction perpendicular to the propagation direction. Also,there should be photonic bands in the direction in which the guidedlight propagates.

INDUSTRIAL APPLICABILITY

As explained above, the present invention can be applied widely tooptical elements that can utilize such effects as dispersioncompensation and optical non-linearity caused by group velocityanomalies of higher-order band propagation light.

1. A photonic crystal optical waveguide, comprising: a optical waveguideportion having a core made of a photonic crystal with a structure havinga periodic refractive index in at least one direction perpendicular to apropagation direction of guided light and having a uniform refractiveindex in the propagation direction of the guided light, and a claddingarranged in contact with the core, in order to confine the guided lightin the core; and an incident-side phase modulation portion arranged inclose proximity or in contact with an incident surface of the core. 2.The photonic crystal optical waveguide according to claim 1, whereinthere is a photonic band in the propagation direction of the light inthe core; wherein the incident-side phase modulation portionphase-modulates incident guided light and lets it propagate through thecore of the optical waveguide portion; and wherein the core propagatesall or at least half of the energy of the phase-modulated guided lightas a wave associated with higher-order photonic bands of said photonicbands.
 3. The photonic crystal optical waveguide according to claim 1,wherein the incident-side phase modulation portion is a phase gratinghaving a refractive index period that is adjusted to the refractiveindex period of the core.
 4. The photonic crystal optical waveguideaccording to claim 1, wherein the incident-side phase modulation portionis a phase grating having the same structure as the core, and having thesame refractive index period as the core.
 5. The photonic crystaloptical waveguide according to claim 1, wherein the incident-side phasemodulation portion is a portion separated by cutting an end portionvicinity on the incident surface side of the core.
 6. The photoniccrystal optical waveguide according to claim 2, wherein the core lets awave associated with the second coupled photonic band from the lowestorder of the phase-modulated guided light propagate.
 7. The photoniccrystal optical waveguide according to claim 1, further comprising anemerging-side phase modulation portion arranged in close proximity or incontact with an emerging surface of the core from which the guided lightemerges.
 8. The photonic crystal optical waveguide according to claim 7,wherein the emerging-side phase modulation portion converts the lightemerging from the emerging surface of the core into a plane wave.
 9. Thephotonic crystal optical waveguide according to claim 7, wherein theemerging-side phase modulation portion is a phase grating having arefractive index period that is adjusted to the refractive index periodof the core.
 10. The photonic crystal optical waveguide according toclaim 7, wherein the emerging-side phase modulation portion is a phasegrating having the same structure as the core, and having the samerefractive index period as the core.
 11. The photonic crystal opticalwaveguide according to claim 7, wherein the emerging-side phasemodulation portion is a portion separated by cutting an end portionvicinity on the emerging surface side of the core.
 12. The photoniccrystal optical waveguide according to claim 1, wherein the cladding ismade of a photonic crystal having a periodic refractive index in atleast one direction perpendicular to a propagation direction of theguided light and having a uniform refractive index in the propagationdirection of the guided light.
 13. The photonic crystal opticalwaveguide according to claim 1, wherein the core comprises an activematerial having an optical non-linear effect.
 14. The photonic crystaloptical waveguide according to claim 1, wherein the core is made of amultilayer film layer having a periodic refractive index in one or twodirections perpendicular to the propagation direction of the guidedlight and having a uniform refractive index in the propagation directionof the guided light.
 15. The photonic crystal optical waveguideaccording to claim 12, wherein the optical waveguide portion has a fibershape with a substantially circular cross section, and the core isfiber-shaped with the cladding formed around the core; and wherein thecore and the cladding have a uniform refractive index in the propagationdirection of the guided light.
 16. The photonic crystal opticalwaveguide according to claim 15, wherein the refractive index periods ofthe core and the cladding are symmetric with respect to the center axisof the optical waveguide portion, which is parallel to the propagationdirection of the guided light.
 17. The photonic crystal opticalwaveguide according to claim 16, wherein the optical waveguide portioncomprises a fiber-shaped homogenous substance with a substantiallycircular cross section, a plurality of cavities are formed in thehomogenous substance along its longitudinal direction, and the pluralityof cavities are formed symmetric to the center axis of the opticalwaveguide portion, which is parallel to the propagation direction of theguided light.
 18. The photonic crystal optical waveguide according toclaim 17, wherein all or some of the cavities are filled with a fluidsubstance.
 19. The photonic crystal optical waveguide according to claim16, wherein the refractive index in the cross section of the opticalwaveguide portion changes periodically and in concentric circles withrespect to a distance from the center axis of the optical waveguideportion, which is parallel to the propagation direction of the guidedlight.